AFM detection of the mechanical resonances of coiled carbon nanotubes

We introduce a method for atomic force microscopy (AFM)-based detection of mechanical resonances in helix-shaped multi-walled carbon nanotubes. After deposition on an oxidized silicon substrate, the three-dimensional structure of suspended nanotubes, which bridges an artificially created step on the surface, can be visualized using AFM operating in the non-contact mode. The suspended coiled nanotubes are resonantly excited, in situ, at the fundamental frequency by an ultrasonic transducer connected to the substrate. When the AFM tip is positioned above the coiled nanotube, the cantilever is unable to follow the fast nanotube oscillations. Nevertheless, an oscillation amplitude-dependent signal is generated due to the non-linear force-to-distance dependence. Measurement of the mechanical resonances of the helix-shaped carbon nanotubes can be used to quantitatively determine their elastic properties. Assuming that a coiled nanotube can be modeled as a suspended helix-shaped uniformly thin elastic beam, the obtained resonance frequency is consistent with a Young's modulus of 0.17ǂ.05 TPa.     

Effect of tip mass on frequency response and sensitivity of AFM cantilever in liquid

The effect of tip mass on the frequency response and sensitivity of atomic force microscope (AFM) cantilever in the liquid environment is investigated. For this purpose, using Euler–Bernoulli beam theory and considering tip mass and hydrodynamic functions in a liquid environment, an expression for the resonance frequencies of AFM cantilever in liquid is derived. Then, based on this expression, the effect of the surface contact stiffness on the flexural mode of a rectangular AFM cantilever in fluid is investigated and compared with the case where the AFM cantilever operates in the air. The results show that in contrast with an air environment, the tip mass has no significant impact on the resonance frequency and sensitivity of the AFM cantilever in the liquid. Hence, analysis of AFM behaviour in liquid environment by neglecting the tip mass is logical.     

Hydrodynamic interaction of AFM cantilevers with solid walls: An investigation based on AFM noise analysis

The European Physical Journal E - The noise power spectrum of the thermally activated motion of an AFM cantilever has been analyzed with respect to viscoelastic and hydrodynamic coupling between...     

Determination of the mass of polymer films using an AFM cantilever

There are no established methods that have a sensitivity during the determination of an adsorbed polymer film mass that is not worse than 1 ng that do not require additional calibration and the usage of reference measures. A highly sensitive method for measuring an adsorbed polymer is proposed in this work. The added mass was determined by the change of the resonance frequency of a cantilever used in atomic-force microscopy (AFM) as a probe. A modification of the cantilever surface is proposed that allows one to avoid the affect of the adsorbed polymer on the cantilever force constant. The mass of poly(diallyldimethylammonium) (PDDA) chloride adsorbed on the cantilever surface was obtained with a sensitivity of 0/01 ng using an AFM cantilever.     

Frequency shifts of cantilever in AFM

The frequency shift and frequency shift image of cantilever in AFM have been studied by numerical integration of the equation of motion of cantilever for silicon tip with rutile TiO₂(0 0 1) surface in UHV conditions and by the Hamaker summation method for the tip-surface interaction forces. The effects of the excitation frequency at the cantilever base and the equilibrium position of the tip on the frequency shift have been calculated and the results showed the same phenomena as those measured, e.g., the frequency shift increased dramatically or rapidly before the contact point and was then almost level off after the contact point. The effects of scanning speed and the initial closest distance of tip to the contact point have been calculated at different excitation frequencies at the cantilever base and the results showed that proper frequency shift image could be obtained either by noncontact mode at the excitation frequency slightly less than the resonance frequency of free cantilever, or by tapping mode at the excitation frequency a few times smaller than the resonance frequency of free cantilever.     

Giant enhancement of noncontact friction between closely spaced bodies by dielectric films and two-dimensional systems

The effect of an external bias voltage and spatial variations of the surface potential on the damping of cantilever vibrations in an atomic force microscope (AFM) is considered. The damping is due to an electrostatic friction that arises due to dissipation of the energy of an electromagnetic field generated in the sample by oscillating static charges induced on the surface of the AFM probe tip by the bias voltage or spatial variations of the surface potential. A similar effect appears when the tip is oscillating in an electrostatic field created by charged defects present in the dielectric sample. The electrostatic friction is compared to the van der Waals (vdW) friction between closely spaced bodies, which is caused by a fluctuating electromagnetic field related to the quantum and thermal fluctuations of current density inside the bodies. It is shown that the electrostatic friction and the vdW friction can be strongly enhanced in the presence of dielectric films or two-dimensional (2D) structures—such as a 2D electron system or an incommensurate layer of adsorbed ions exhibiting acoustic oscillations—on the probe tip and sample surfaces. It is also shown that the damping of cantilever oscillations caused by the electrostatic friction in the presence of such 2D structures can have the same order of magnitude and the same dependence on the distance as observed in experiment by Stipe et al. [Phys. Rev. Lett. 87, 096801 (2001)]. At small distances, the vdW friction can be large enough to be measured in experiment. In interpreting the experimental data that obey a quadratic dependence on the bias voltage, one can reject a phonon mechanism according to which the friction depends on the fourth power of the voltage.     

Numerical study of the hydrodynamic drag force in atomic force microscopy measurements undertaken in fluids

When atomic force microscopy (AFM) is employed for in vivo study of immersed biological samples, the fluid medium presents additional complexities, not least of which is the hydrodynamic drag force due to viscous friction of the cantilever with the liquid. This force should be considered when interpreting experimental results and any calculated material properties. In this paper, a numerical model is presented to study the influence of the drag force on experimental data obtained from AFM measurements using computational fluid dynamics (CFD) simulation. The model provides quantification of the drag force in AFM measurements of soft specimens in fluids.The numerical predictions were compared with experimental data obtained using AFM with a V-shaped cantilever fitted with a pyramidal tip. Tip velocities ranging from 1.05 to 105 μm/s were employed in water, polyethylene glycol and glycerol with the platform approaching from a distance of 6000 nm. The model was also compared with an existing analytical model. Good agreement was observed between numerical results, experiments and analytical predictions. Accurate predictions were obtained without the need for extrapolation of experimental data. In addition, the model can be employed over the range of tip geometries and velocities typically utilized in AFM measurements.     

基于AFM的固液界面表面电荷密度测量方法

固液界面的表面电荷会影响微纳流体系统的流体阻力,因此如何测量固液界面的表面电荷密度以及分析表面电荷的产生机理对于研究表面电荷对流体阻力的影响具有较大的意义。提出了一种基于接触式AFM的固液界面表面电荷密度测量方法。基于该方法测量了浸在去离子水和0.01 mol/L的NaCl溶液中的高硼硅玻璃和二氧化硅样本的表面电荷密度,并研究了溶液pH值对表面电荷的影响。研究结果表明高硼硅玻璃和二氧化硅由于表面硅烷基的电离带负电。溶液pH值和离子浓度的增加都会增加浸在去离子水和0.01 mol/L的NaCl溶液中高硼硅玻璃和二氧化硅的表面电荷密度的绝对值。     

Lattice-resolution imaging of the sapphire (0 0 0 1) surface in air by AFM

Lattice-resolution images of single-crystal α-alumina (sapphire) (0 0 0 1) surfaces have been obtained using contact-mode AFM under ambient conditions. It was found that the hexagonal surface lattice has a periodicity of 0.47 ± 0.11 nm, which is identical to that reported previously when the same surface was imaged in water. Large lattice corrugations (as high as 1 nm) were observed, but were concluded to be imaging artifacts because of the strong friction which causes additional deflection of the cantilever. The additional deflection of the cantilever is registered by the detector of the optical beam-deflection AFM resulting in an overestimation of the height at each lattice point. Abrupt changes were also resolved in the topography including honeycomb patterns and a transition from 2D lattices to 1D parallel stripes, with scanning direction. These phenomena can be explained by the commensurate sliding between the tip and sapphire surface due to the strong contact force.     

Hydrodynamic scaling law in undulatory braking locomotion

Flow over a fish-like airfoil is numerically investigated to elaborate the hydrodynamics of the undulatory braking locomotion for an elongated eel-like body or long-based fin. For undulation with low frequency, we find that boundary layer separation occurs in a parameter region with wakes in which two vortex pairs are formed per undulatory period. The physical mechanism of separation is governed by the slip(the ratio of swimming-to-body-wave speed), and the critical value of the slip in an inertial flow regime is approximately 4/3 rather than 1, which is independent of steepness(or amplitude). The relationship between pressure drag and relative velocity(between phase speed and free stream velocity) changes from linear to quadratic, corresponding to two different flow structures; this happens due to boundary layer separation, and the piecewise scaling relationship between pressure drag and relative velocity is explicitly clarified. Considering the viscosity effects, the separation criterion and the scaling relationship in the case of an undulatory brake are both synthetically modified using the Reynolds number, with all the required parameters clearly expressed. The results of this study provide physical insight into understanding the flow structures and hydrodynamics of the undulatory braking locomotion, which has instructional significance to brake design.     

Normal and Lateral Force Calibration Techniques for AFM Cantilevers

Atomic force microscopy (AFM) is a useful tool, not only for imaging but also for quantification of normal and lateral forces exerted on the AFM tip while interacting with the surface of materials. In order to measure these forces, an accurate determination of the normal and lateral forces exerted on the AFM cantilever is necessary. To date, there is no generally accepted technique for the force calibration of AFM cantilevers. In this paper, we present a critical review of various techniques for measuring cantilever stiffness in the normal and lateral/torsional directions in order to calibrate the normal and lateral forces exerted on AFM cantilevers. The key concepts of each technique are presented, along with a discussion of their advantages and disadvantages. An understanding of the issues involved in the determination of the stiffness is needed for the proper choice and implementation of any given technique.     

Morphology of alkali halide thin films studied by AFM

Thin layers of alkali halides were investigated by atomic force microscope (AFM). The studied systems were: LiBr/KBr(0 0 1) with −16.7% misfit, LiF/Si(0 0 1) with +4.4% misfit, LiBr/LiF(0 0 1) with +36.8% misfit and NaCl/Si(0 0 1) with +46.5% misfit. The results show that the surface morphology strongly depends on the temperature of layer formation. The alkali halides deposited on the foreign substrate at elevated temperatures or at room temperature and subsequently annealed form preferentially 3D islands leaving uncovered substrate areas between them. It is suggested that Ostwald ripening takes place at elevated temperatures.     

Mechano-chemical AFM nanolithography of metallic thin films: A statistical analysis

A mechano-chemical atomic force microscope (AFM) nanolithography on a metallic thin film (50 nm in thickness) covered by a spin-coated soft polymeric mask layer (50–60 nm in thickness) has been introduced. The surface stochastic properties of initial grooves mechanically patterned on the mask layer (grooves before chemical wet-etching) and the lithographed patterns on the metallic thin film (the grooves after chemical wet-etching) have been investigated and compared by using the structure factor, power spectral density, and AFM tip deconvolution analyses. The effective shape of cross section of the before and after etching grooves have been determined by using the tip deconvolution surface analysis. The wet-etching process improved the shape of the grooves and also smoothed the surface within them. We have indicated that relaxation of the surface tension of the deposited mask layer after the AFM scribing is independent from surface density of the grooves and also their length scale. Based on the statistical analysis, it was found that increase of the width of the grooves after the wet-etching and also relaxation of surface tension of the mask layer resulted in a down limit in the size of the metallic nanowires made by the combined nanolithography method. An extrapolation of the analyzed statistical data has indicated that, in this method, the minimum obtainable width and length of the metallic nanowires are about 55 nm and 2 μm, respectively.     

Primary information sensors for AFM based on quasiparticle flows

A new class of experimental techniques is presented which allows the behavior of elementary collective excitations (quasiparticles) in solids to be studied at the mesoscopic scale. New experimental equipment is being constructed in the classical scheme of an atomic force microscope in which the sensor of primary information is a cantilever. The defining feature of the proposed sensor based on a cantilever is the addition of a generator and detector of quasiparticles to its design. The generator is located either on the tip of the cantilever or in close proximity to the needle on the cantilever, so that the flow of quasiparticles emitted by the generator propagates along the needle of the cantilever to the point where the needle tip touches the surface. The detector is located in a similar way. The measured quantity is the reflection coefficient of the flux of quasiparticles from the interface between the cantilever needle tip and the surface being scanned.     

AFM study of BSA adlayers on Au stripes

Thin narrow Au stripes suitable for propagating long-range surface plasmon-polaritons were deposited by evaporation and lift-off on a thermal oxide layer on a silicon substrate, and modified by direct adsorption of bovine serum albumin (BSA). Atomic force microscopy (AFM) measurements reveal that BSA adsorbs onto the Au stripes from phosphate buffer solutions forming an adlayer having an average thickness of about 2 nm (surface mass density of about 2 ng/mm²). Comparisons with a simple adsorption model suggest the side-on adsorption of a single monolayer of BSA followed by denaturation and flattening. The BSA-coated stripes have an increased surface roughness compared to a virgin stripe.     

Mechanical properties of hexagonal boron nitride synthesized from film of Cu/BN mixture by surface segregation

Hexagonal boron nitride (h-BN) has a low friction coefficient and weak surface attractive force similar to graphite. Furthermore, while graphite is conductive, BN is a good insulator. These properties make it suitable for application like lubricating coating or as an insulator/buffer layer in electronic devices. The synthesize of h-BN layer by surface segregation phenomena and mechanical properties of the h-BN surface segregated on Cu substrate have been investigated. During in situ annealing, the surface segregation of BN occurred on Cu/BN film deposited by deposition process with a rf magnetron co-sputtering system. Auger electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS) analysis showed that though the h-BN layer synthesized was not covered whole area of substrate but the h-BN layers partially covered substrate. And the concentration of oxygen on the surface after exposure in air is decreased with increase of BN concentration. The topography of atomic forces microscopy (AFM) showed that h-BN phases surface segregated are discontinuous droplet shape. The force curves of AFM and friction force of lateral force microscopy (LFM) showed that the h-BN droplet surface segregated have very weak attractive force and low friction coefficient equal to h-BN sintered plate.     

Surface defects characterization with frequency and force modulation atomic force microscopy using molecular dynamics simulations

This paper is devoted to the characterization of the surface defects using a recently developed AFM technique called frequency and force modulation AFM (FFM–AFM). The simulated system includes a recently developed gold coated AFM probe which interacts with a sample including single-atom vacancy and impurities. In order to examine the behavior of the above system on different transition metals, the molecular dynamics (MD) simulation with Sutton–Chen (SC) inter-atomic potential is used. In this study, an online imaging simulation of the probe and sample is performed, and the effects of the horizontal scan speed, the effective frequency set-point, the cantilever stiffness, the tip-sample rest position and the cantilever quality factor on the resulting images are investigated. Using a proposed optimum controlling scheme for the excitation force amplitude, the cantilever horizontal speed can be increased.     

Modeling diffusion of adsorbed polymer with explicit solvent

Computer simulations of a polymer chain of length N strongly adsorbed at the solid-liquid interface in the presence of explicit solvent are used to delineate the factors affecting the N dependence of the polymer lateral diffusion coefficient, D(||). We find that surface roughness has a large influence, and D(||) scales as D(||) approximately N(-x), with x approximately 3/4 and x approximately 1 for ideal smooth and corrugated surfaces, respectively. The first result is consistent with the hydrodynamics of a "particle" of radius of gyration R(G) approximately N(nu) (nu=0.75) translating parallel to a planar interface, while the second implies that the friction of the adsorbed chains dominates. These results are discussed in the context of recent measurements.     

Changes in surface stress, morphology and chemical composition of silica and silicon nitride surfaces during the etching by gaseous HF acid

HF acid attack of SiO₂ and Si₃N₄ substrates is analyzed to improve the sensitivity of a sensor based on microcantilever. Ex situ analysis of the etching using XPS, SIMS and AFM show significant changes in the anisotropy and the rate of the etching of the oxides on SiO₂ and Si₃N₄ surface. Those differences influence the kinetic evolution of the plastic bending deflection of the cantilever coated with SiO₂ and Si₃N₄ layer, respectively. The linear dependence between the HF concentration and the Si₃N₄ cantilever bending corresponds to a deep attack of the layer whereas the non-linear behavior observed for SiO₂ layer can be explained by a combination of deep and lateral etching. The cantilever bending is discussed in terms of free surface energy, layer thickness and grain size.     

Estimating material viscoelastic properties based on surface wave measurements: a comparison of techniques and modeling assumptions

Previous studies of the first author and others have focused on low audible frequency (<1 kHz) shear and surface wave motion in and on a viscoelastic material comprised of or representative of soft biological tissue. A specific case considered has been surface (Rayleigh) wave motion caused by a circular disk located on the surface and oscillating normal to it. Different approaches to identifying the type and coefficients of a viscoelastic model of the material based on these measurements have been proposed. One approach has been to optimize coefficients in an assumed viscoelastic model type to match measurements of the frequency-dependent Rayleigh wave speed. Another approach has been to optimize coefficients in an assumed viscoelastic model type to match the complex-valued frequency response function (FRF) between the excitation location and points at known radial distances from it. In the present article, the relative merits of these approaches are explored theoretically, computationally, and experimentally. It is concluded that matching the complex-valued FRF may provide a better estimate of the viscoelastic model type and parameter values; though, as the studies herein show, there are inherent limitations to identifying viscoelastic properties based on surface wave measurements.